Derivation of some solitary wave solutions for the (3+1)- dimensional pKP-BKP equation via the IME tanh function method

Abeer S. Khalifa; Hamdy M. Ahmed; Niveen M. Badra; Jalil Manafian; Khaled H. Mahmoud; Kottakkaran Sooppy Nisar; Wafaa B. Rabie; Abeer S. Khalifa; Hamdy M. Ahmed; Niveen M. Badra; Jalil Manafian; Khaled H. Mahmoud; Kottakkaran Sooppy Nisar; Wafaa B. Rabie

doi:10.3934/math.20241345

AIMS Mathematics

2024, Volume 9, Issue 10: 27704-27720. doi: 10.3934/math.20241345

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Derivation of some solitary wave solutions for the (3+1)- dimensional pKP-BKP equation via the IME tanh function method

1.
Department of Physics and Engineering Mathematics, Faculty of Engineering, Ain Shams University, Abbassia, Cairo, Egypt
2.
Department of Mathematics, Faculty of Basic Sciences, The German University in Cairo (GUC), Cairo, Egypt
3.
Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El Shorouk Academy, Cairo, Egypt
4.
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
5.
Natural Sciences Faculty, Lankaran State University, 50, H. Aslanov str., Lankaran, Azerbaijan
6.
Department of Physics, College of Khurma University College, Taif University, Taif 21944, Saudi Arabia
7.
Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia
8.
Department of Engineering Mathematics and Physics, Higher Institute of Engineering and Technology, Tanta, Egypt

Received: 29 August 2024 Revised: 11 September 2024 Accepted: 14 September 2024 Published: 25 September 2024
MSC : 35B35, 35C07, 35C08, 35C09

This study is focusing on the integrable (3+1)-dimensional equation that combines the potential Kadomtsev-Petviashvili (pKP) equation with B-type Kadomtsev-Petviashvili (BKP) equation, also known as the pKP-BKP equation. The idea of combining integrable equations has the potential to produce a variety of unexpected outcomes such as resonance of solitons. This article provides a wide range of alternative exact solutions for the pKP-BKP equation in three dimensional form, including dark solitons, singular solitons, singular periodic solutions, Jacobi elliptic function (JEF) solutions, rational solutions and exponential solution. The improved modified extended (IME) tanh function method is employed to investigate these solutions. All of the obtained solutions for the investigated model are presented using the Wolfram Mathematica program. To further help in understanding the solutions' physical characteristics and dynamic structure, the article provides visual representations of some derived solutions using 2D representation in addition to the 3D graphs via symbolic computation. This article aims to use a potent strategy using a powerful scheme to derive different solutions with various structures. Additionally, the results greatly improve and enhance the literature's solutions to a combined pKP-BKP equation and allow deep understanding of the nonlinear dynamic system through different exact solutions.
- potential Kadomtsev-Petviashvili-B-type Kadomtsev-Petviashvili,
- NPDE,
- IME tanh function method,
- solitary wave solutions
Citation: Abeer S. Khalifa, Hamdy M. Ahmed, Niveen M. Badra, Jalil Manafian, Khaled H. Mahmoud, Kottakkaran Sooppy Nisar, Wafaa B. Rabie. Derivation of some solitary wave solutions for the (3+1)- dimensional pKP-BKP equation via the IME tanh function method[J]. AIMS Mathematics, 2024, 9(10): 27704-27720. doi: 10.3934/math.20241345

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Abstract

This study is focusing on the integrable (3+1)-dimensional equation that combines the potential Kadomtsev-Petviashvili (pKP) equation with B-type Kadomtsev-Petviashvili (BKP) equation, also known as the pKP-BKP equation. The idea of combining integrable equations has the potential to produce a variety of unexpected outcomes such as resonance of solitons. This article provides a wide range of alternative exact solutions for the pKP-BKP equation in three dimensional form, including dark solitons, singular solitons, singular periodic solutions, Jacobi elliptic function (JEF) solutions, rational solutions and exponential solution. The improved modified extended (IME) tanh function method is employed to investigate these solutions. All of the obtained solutions for the investigated model are presented using the Wolfram Mathematica program. To further help in understanding the solutions' physical characteristics and dynamic structure, the article provides visual representations of some derived solutions using 2D representation in addition to the 3D graphs via symbolic computation. This article aims to use a potent strategy using a powerful scheme to derive different solutions with various structures. Additionally, the results greatly improve and enhance the literature's solutions to a combined pKP-BKP equation and allow deep understanding of the nonlinear dynamic system through different exact solutions.

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